Finite impulse response (FIR) filters are one of the most important areas of study and implementation in digital signal processing. As such, this tutorial is aimed at those readers who already know the basic operation and properties of FIR filters, but want to go a little further and understand some specific FIR filter algorithms and their implementation in modern DSP systems. Here we’ll introduce minimum-phase, matched, comb, halfband, and complex FIR filters. We’ll also discuss aspects of converting lowpass FIR filters to bandpass filters. We’ll consider a few popular implementation schemes for improving the functional efficiency, and reducing the hardware complexity, of FIR filters. In addition, in this DSP Workshop paper you’ll learn several FIR filter buzzwords you can use at cocktail parties to impress your immediate supervisor.

This “second look” at FIR filters assumes the reader understands the fundamental operation of traditional garden-variety FIR filters and their transversal data flow, convolution properties, linear phase, and constant group delay.